Gibson was expected to get the tie at Melbourne's John Cain Arena off to a flying start on Friday, but she was a shock loser 7-6 (7-4) 7-5 against the lowly ranked 17-year-old.
Kimberly Birrell was then unable to get the home team back on level pegging, going down 4-6 6-3 6-3 against top-ranked Brit Harriet Dart.
That leaves experienced pair Storm Hunter and Ellen Perez needing to win the doubles in the opening match on Saturday for Australia to remain alive in the tie.
World No.56 Gibson took over as the leading local following injury to Maya Joint and arrived at the tie in sparkling form.
The 21-year-old had recently beaten five top 20-ranked players and rocketed to her career-high ranking.
With the visitors missing their four best players, the Australians were hot favourites to advance to the Finals in China in September, but that was quickly dismissed by big-serving Stojsavljevic.Â
"It's my first time playing a match in the Billie Jean King Cup for Team Australia, so there was obviously some nerves out there today and not the way I would have liked to have played and not the result that I would have liked to have had happened," Perth product Gibson said.
"Credit to Mika, she came out playing really well, served amazing, so I did my best with what I was able to bring today, but unfortunately it wasn't enough."
Gibson had a nervous start against the 2024 US Open junior champion, before clawing her way back to level at 3-3 and pushing the first set to a tiebreak.
But world No.275 Stojsavljevic steamed through the decider and closed it out 7-4 on a backhand error by her rival.
The young Brit carried that momentum into the second set, going ahead 5-2, before powerhouse Gibson found her touch and broke her twice to level at 5-5.
Stojsavljevic sent down three aces in her haul of 12 for the match to survive a marathon game, including five break points, then broke Gibson again to wrap up the match.
World No.80 Birrell was on track to level for the Australians, taking the first set, but lost momentum against against the gritty 173-ranked Dart.
The pair exchanged breaks in the third set but Dart broke again to lead 4-3 and wasn't troubled from that point.
Dart will partner Jodie Burrage in Saturday's live doubles match, with the reverse singles scheduled for later in the day.
